Search Results for author: Zhiqin Lu

Found 6 papers, 0 papers with code

Eigenvalue Estimates on Bakry-Emery Manifolds

no code implementations11 Dec 2020 Nelia Charalambous, Zhiqin Lu, Julie Rowlett

We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary.

Spectral Theory Analysis of PDEs Differential Geometry

One can hear the corners of a drum

no code implementations11 Dec 2020 Zhiqin Lu, Julie Rowlett

We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be isospectral to any connected domain, of any genus, which has smooth boundary.

Spectral Theory Mathematical Physics Analysis of PDEs Differential Geometry Mathematical Physics 35P99 (primary), 35K05 (secondary)

The sound of symmetry

no code implementations10 Dec 2020 Zhiqin Lu, Julie Rowlett

Following the introduction, the main techniques used in inverse isospectral problems are collected and discussed.

Spectral Theory Analysis of PDEs Differential Geometry primary 58C40, secondary 35P99

Learning in the Machine: the Symmetries of the Deep Learning Channel

no code implementations22 Dec 2017 Pierre Baldi, Peter Sadowski, Zhiqin Lu

Specifically, random backpropagation and its variations can be performed with the same non-linear neurons used in the main input-output forward channel, and the connections in the learning channel can be adapted using the same algorithm used in the forward channel, removing the need for any specialized hardware in the learning channel.

Learning in the Machine: Random Backpropagation and the Deep Learning Channel

no code implementations8 Dec 2016 Pierre Baldi, Peter Sadowski, Zhiqin Lu

It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system.

Complex-Valued Autoencoders

no code implementations20 Aug 2011 Pierre Baldi, Zhiqin Lu

The general framework described here is useful to classify autoencoders and identify general common properties that ought to be investigated for each class, illuminating some of the connections between information theory, unsupervised learning, clustering, Hebbian learning, and autoencoders.

Clustering

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